Full wavefield inversion (FWI) is a computer-implemented geophysical method that is recently being used to invert for subsurface properties such as velocity or acoustic impedance. FWI is known to estimate the subsurface properties more accurately than, for example, inversion of the recorded wavefield after being processed to eliminate multiple reflections. The crux of any FWI algorithm can be described as follows: using a starting subsurface property model, synthetic seismic data are generated, i.e. modeled or simulated, by solving the wave equation using a numerical scheme (e.g., finite-difference, finite-element etc.). The synthetic seismic data are compared with the field seismic data and using the difference between the two, an error or objective function is calculated. Using the objective function, a modified subsurface model is generated which is used to simulate a new set of synthetic seismic data. This new set of synthetic seismic data is compared with the field data to generate a new objective function. This process is repeated until the objective function is satisfactorily minimized and the final subsurface model is generated. A global or local optimization method is used to minimize the objective function and to update the subsurface model. The accuracy of any FWI method is in general dictated by its two important components: the numerical algorithm used for solving wave equation to generate synthetic seismic data and the optimization scheme. Depending on the type of optimization scheme employed, a FWI method may get stuck in a local minimum while updating the subsurface model.
There are several numerical methods such as finite-difference, finite-element etc. available for solving the wave equation. The finite-difference methods [1] which are the most popular numerical scheme for solving the wave equation suffer from the interface error generated by the misalignment between numerical grids and numerical interfaces [2]. Although all types of reflection (primaries, free-surface multiples, internal multiples etc.) suffer from the interface error, the free-surface multiples are affected the most due to multiple bounces between the free surface and reflectors in subsurface. Given that free-surface multiples are some of the strongest arrivals in a seismic record, including free-surface multiples in a FWI workflow may result in erroneous inverted subsurface properties.
Although in any seismic experiment, full wavefield (primaries, internal multiples and free-surface multiples) are acquired, due to inability of accurately modeling free-surface multiples, in most of the FWI methods only primaries and internal multiples are used to invert for subsurface models. Given that the free-surface multiples carry additional information about the subsurface model and complements to the information being carried by primaries and internal multiples, it is expected that including free-surface multiples in inversion will improve the accuracy of the inverted subsurface model. The present invention is a method that permits circumventing the direct modeling and subtraction of free-surface multiples.